This invention relates to a shear stress gauge for measuring fluctuating shear stress created on a wall by fluid flow over the wall. The gauge is particularly applicable to the measurement of mean and fluctuating shear stress components under a turbulent boundary layer.
A variety of techniques have been used for the measurement of wall shear stress. For mean wall shear stress measurement, it is customary to use a Preston tube. This technique depends upon the assumption of a wall law for the flow. This law applies only for equilibrium boundary layers and is not valid for many turbulent or transitional flows. Surface hot film gauges have become very popular in recent years, largely because of their simplicity in installation. Such gauges are never calibrated by the manufacturer; calibration must be done by the individual investigator. As a result, most hot film gauge measurements are qualitative in nature rather than quantitative. The heat transfer characteristics of the substrate adjacent to such gauges are very important to their performance, particularly in air.
Certain other techniques such as the photographing of path lines created with fluorescent dyes, and electro-chemical methods have been used from time to time to measure wall shear stress. Only two present techniques for measurement are linear: the floating element surface gauge and the pulsed wire gauge. The deflection of the floating element surface gauge is determined by a capacitance or similar measurement. This gauge has a serious deficiency in that it must have a peripheral gap separating it from the adjacent wall. A mean pressure gradient in the outer flow will cause fluid flow in the gap which results in the gauge responding erroneously to differential gap pressure. The pulsed wire gauge measures the time it takes for a heated spot of fluid generated at one wire to convect to a second sensing wire downstream, thus determining the streamwise flow velocity very near the wall. Both the floating element and the pulsed wire gauges have very limited dynamic response and spatial resolution. In addition to the qualitative nature of the measurements utilizing hot film gauges, these gauges are incapable of detecting flow reversal. Moreover, because of their nonlinearity, mean flow measurements are highly contaminated by the large fluctuating shear component at the wall under a turbulent boundary layer. Therefore, they can be calibrated only in a fully developed turbulent flow.
Measurements of unsteady wall shear stress by various known techniques show a tremendous scatter for the same type of flow. The spread in the ratio of mean square shear stress to mean wall shear stress is from 5% to 50%, depending on which experimental technique is used. At the wall, one is dealing with something very different from the conventional hot wire measurement in the main portion of the boundary layer. There the largest ratio of r.m.s. to mean is customarily of the order of 5%. At the wall, when a nonlinear device is used, such as for all techniques except the floating element and pulsed wire methods, the fact that the fluctuating wall shear stress value is a very high fraction of the mean shear stress implies that the mean measurement itself is badly contaminated by the turbulence. It has been customary in the past to calibrate Preston tubes and hot film gauges by comparing their output to the pressure drop in fully developed turbulent pipe flow. Clearly, this technique is not really valid in any other type of turbulent flow except one with the same dynamic characteristics as the pipe flow itself.